Taking the Headlines article and the classes of a typical high school mathematics student, how many of the headlines would a a student understand?

At the very least, understanding the entire list requires knowing about: correlation vs. causation, inflation, experimental replication, estimation of large numbers, incompatibility of comparisons with different conditions, understanding how tax brackets work, meaninglessness of predictions within a margin of error, statistically unlikely events, and reversion to the mean.

None of these will ever occur in an traditional math class. In other words, in the list of supposed math literacies, the typical math student in the US receives zero of them. (Some might possibly show up in a class labelled “Economics” or “Free Enterprise”, but those don’t get called Math Classes).

It’d be fair to argue I’m being highly specific in my starting definitions, but I often see the “good citizen” argument used during a general “why are we teaching math” type discussion which assumes a traditional math class track. That sort of argument only works if people are prepared to also overhaul the curriculum (by putting, for example, statistics before calculus as Arthur Benjamin discusses at TED).

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This is a very good point, however, we seem to be quite literate in (most of) these things without having been explicitly taught them. In much the same way that we eventually gain a very large vocabulary without having to look up each and every word in a dictionary, although we have to look up some. I have often pointed out turn of the century textbooks because of they were full of situational word problems with new terms introduced as the chapters wore on. Granted, these century old texts are too computational for modern times, but their use of word problems in many contexts and situations is still a valuable ingredient. This is something I have stressed from the beginning with my son and it shows now with his ability to pick up on the intended arithmetic relationships in situations involving new terms. I am not suggesting that he is at the level of sophistication of your examples, yet. He is only in 5th grade and I think your examples are probably more high school age. But he is on that track.

In any event, I like your point about mathematical literacy and being able to recognize and interpret the arithmetical meaning in such text. I disagree that it doesn’t occur in traditional (or even non traditional) classes. Someone wrote those headlines.:) I think it has to do with whether the curriculum develops sophistication in the student or not. And that type of development takes place year over year and is unfortunately very neglected today due to the manner in which elementary math has been broken down into tiny disconnected pieces (standards).

I have a book, “Foundations of Advanced Mathematics” from 1959 that is actually like your proposal, although it is written in such a way that the teacher can choose the order. It assumes that the student has taken algebra and plane geometry. The table of contents is…

It doesn’t treat logic and proofs, which I assume would have to fit in with geometry. It isn’t a doorstop sized book either. Only 500 pages, but quite dense. Obviously a multi-year book, and even then I think the material is presented too deeply for a high school student to make it through all of it. The introduction states that a teacher would choose the topics they wanted to cover.

My Algebra 2 book (Dolciani, 1970’s), and many honors algebra books from that era include many of your topics (sans calculus and geometry). They too would have to be used over a couple of years to cover everything.

In your list I think I would move combinatorics to be with statistics and logic and proofs to be with geometry. No particular reason other than to even it out some.

It is common to put combinatorics and statistics together, but that results in confusion on students’ part, because too many of the probability examples are uniform distribution counting problems. I’ve always felt that putting proofs together with geometry does damage to both. Analytic geometry is much more useful nowadays than Euclidean-style proofs, so I’d rather put geometry with trigonometry and complex numbers.